Question

A rigid body of mass 'm' and radius 'r' rolls without slipping on a rough horizontal surface. A force is acting on a point 'x' distance from the center as shown in figure. Assuming the moment of inertia of the solid body about an axis through its COM be $I_{CM}$. Find the value of x so that static friction is zero.

• A. $\frac{I_{CM}}{r}$
• B. $\frac{I_{CM}}{mr}$
• C. $\frac{I_{CM}}{m{r}^2}$
• D. $\frac{I_{CM}}{m^{2}r}$

Answer 1

The correct option is B

$\frac{I_{CM}}{mr}$

Torque about centre of mass = $F\alpha =I_{CM}\alpha$

But F = ma and a = r$\alpha$

$\Rightarrow mr\alpha x=I_{CM}\alpha$

$x=\frac{I_{CM}}{mr}$